| Nathan Scholfield - 1845 - 232 páginas
...proposition, a sin. A.~ c b sin. 68 FROPOSITION III. In any plane triangle, the sum of any two sides, **is to their difference, as the tangent of half the sum of the** angles opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle,... | |
| John Playfair - 1846 - 317 páginas
...difference as the radius to the tangent of the difference between either of them and 45°. PROP. IV. THEOR. **The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the** angles opposite to those sides, to the tangent of half their difference. Let ABC be any plane triangle... | |
| Dennis M'Curdy - 1846 - 138 páginas
...triangle EFG, BC is drawn parallel to FG the base EC : CF : : EB : BG; that is, the sum of two sides **is to their difference, as the tangent of half the sum of the** angles at the base ia to the tangent of half their difference. * Moreover, the angles DBF, BFE are... | |
| Jeremiah Day - 1848 - 153 páginas
...THE SUM OF THE OPPOSITE ANGLES ; TO THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, **is to their difference ; as the tangent of half the sum of the** angles ACB and ABC, to the tangent of half then- difference. Demonstration. Extend CA to G, making... | |
| George Clinton Whitlock - 1848 - 324 páginas
...A + sin5 : sinlA — sin 7?, or (333) a + b : a—b : : tani(A+B) : tan^(^-S) ; ie PROPOSITION VI. **The sum of any two sides of a triangle is to their** dif- (396) ference, as the tangent of the half sum of the angles opposite to the tangent of half their... | |
| Charles Davies - 1849 - 359 páginas
...+c 2 —a 2 ) = R« x -R- x " * Hence THEOREM V. In every rectilineal triangle, the sum of two sides **is to their difference as the tangent of half the sum of the** angles opposite those sides, to the tangent of half their difference. * For. AB : BC : : sin C : sin... | |
| Jeremiah Day - 1851
...THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) **is to their difference ; as the tangent of half the sum of the** angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making... | |
| A. M. LEGENDRE - 1852
...AC :: sin 0 : sin jR THEOEEM II. In any triangle, the sum of the two sides containing either angle, **is to their difference, as the tangent of half the sum of the** two other angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will AJ3... | |
| Charles Davies - 1886 - 324 páginas
...C : sin B. Theorems. THEOREM 11. In any triangle, the sum of the two sides containing eithe1 angle, **is to their difference, as the tangent of half the sum of** (he t1eo other angles, to the tangent of half their di/ereMe. Let ACB be a triangle: then will With... | |
| Jeremiah Day - 1853 - 5 páginas
...of their opposite angles. It follows, therefore, from the preceding proposition, (Alg. 38'.>.) that **the sum of any two sides of a. triangle, is to their difference ; as the tangent of half the sum of** tin; opposite angles, to the tangent of half their difference. This is the second theorem npplied to... | |
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